sin 0 = cos 0 = tan 8 = y 8 6 4 2 0 2 6 8 X Sin , cos , and tan 8.
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
Related questions
Question
![### Trigonometric Values in Standard Position
In the following diagram, angle \( \theta \) is in standard position. In each case, find \( \sin \theta \), \( \cos \theta \), and \( \tan \theta \).
**sin \( \theta \) =**
[Text Box]
**cos \( \theta \) =**
[Text Box]
**tan \( \theta \) =**
[Text Box]
---
### Diagram Explanation:
#### Graph Description:
- **Axes**:
- The \( y \)-axis is vertical and extends from 0 to 8.
- The \( x \)-axis is horizontal and extends from 0 to 8.
- **Line**:
- A red line originates from the origin (0,0) and extends into the first quadrant, ending at the point (4,8).
- This line represents the terminal side of the angle \( \theta \).
- **Angle**:
- The angle \( \theta \) is formed between the positive \( x \)-axis and the red line.
### Finding Trigonometric Values:
To find \( \sin \theta \), \( \cos \theta \), and \( \tan \theta \):
1. **Calculate the hypotenuse**:
- Using the Pythagorean theorem: \( \text{hypotenuse} = \sqrt{x^2 + y^2} \)
- Here, \( x = 4 \) and \( y = 8 \), so:
\[
\text{hypotenuse} = \sqrt{4^2 + 8^2} = \sqrt{16 + 64} = \sqrt{80} = 4\sqrt{5}
\]
2. **Calculate \( \sin \theta \)**:
\[
\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{8}{4\sqrt{5}} = \frac{2}{\sqrt{5}} = \frac{2\sqrt{5}}{5}
\]
3. **Calculate \( \cos \theta \)**:
\[
\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{4}{4\sqrt{5}} = \frac{1}{\sqrt{5](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb77dd63d-90e0-4a84-b222-b885a237b41a%2F83aee2a0-3898-4c0b-a8dd-5f84460fc8c3%2F6i1jovs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Trigonometric Values in Standard Position
In the following diagram, angle \( \theta \) is in standard position. In each case, find \( \sin \theta \), \( \cos \theta \), and \( \tan \theta \).
**sin \( \theta \) =**
[Text Box]
**cos \( \theta \) =**
[Text Box]
**tan \( \theta \) =**
[Text Box]
---
### Diagram Explanation:
#### Graph Description:
- **Axes**:
- The \( y \)-axis is vertical and extends from 0 to 8.
- The \( x \)-axis is horizontal and extends from 0 to 8.
- **Line**:
- A red line originates from the origin (0,0) and extends into the first quadrant, ending at the point (4,8).
- This line represents the terminal side of the angle \( \theta \).
- **Angle**:
- The angle \( \theta \) is formed between the positive \( x \)-axis and the red line.
### Finding Trigonometric Values:
To find \( \sin \theta \), \( \cos \theta \), and \( \tan \theta \):
1. **Calculate the hypotenuse**:
- Using the Pythagorean theorem: \( \text{hypotenuse} = \sqrt{x^2 + y^2} \)
- Here, \( x = 4 \) and \( y = 8 \), so:
\[
\text{hypotenuse} = \sqrt{4^2 + 8^2} = \sqrt{16 + 64} = \sqrt{80} = 4\sqrt{5}
\]
2. **Calculate \( \sin \theta \)**:
\[
\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{8}{4\sqrt{5}} = \frac{2}{\sqrt{5}} = \frac{2\sqrt{5}}{5}
\]
3. **Calculate \( \cos \theta \)**:
\[
\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{4}{4\sqrt{5}} = \frac{1}{\sqrt{5
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